The resonant frequency of a quartz crystal is dependent on the elastic coefficients, the density, the thickness and overtone operation of the crystal. In addition, each of these factors vary with changes in the ambient temperature of the crystal, and, thus, resonant frequency variations occur.
Conventional methods for making the frequency of a quartz crystal resonator minimally dependent on temperature variations included three approaches. The first approach utilizes a heated oven to control the ambient temperature of the crystal resonator and thus control the frequency of that crystal. To further improve the frequency-temperature performance, the crystal resonator will typically be cut in one of the thermally compensated orientations for which the crystal resonator has inherently good frequency stability over a narrow temperature range. Two widely used singly rotated orientations are the AT and BT.
This approach generally yields crystal resonator controlled oscillators exhibiting the highest frequency stability currently obtainable. However, this approach experiences three potential drawbacks. First, in modern crystal resonator controlled applications, the oven will be the predominant power user. Second, a thermal stabilization time of many minutes is required when the crystal oven is first turned on even when available power is not limited. A large portion of this time is necessary to allow thermal gradients in the resonator to equilibriate and thus the advantage of instant warm up of transistor circuits is lost. Third, optimum temperature control of the quartz resonators is not possible unless the actual temperature of the quartz plate is known. Because the thermal sensing element is not in intimate contact with the resonator, errors in ambient control degrade frequency stability.
The second and third approaches utilize temperature compensation without the use of the oven. VCXO's (Voltage Controlled Crystal Oscillators) and TCXO's (Temperature Controlled Crystal Oscillators) represent the second approach. The VXCO typically includes a combination of a crystal resonator, an amplifier, and a voltage variable phase shifter. The voltage which is applied to the variable phase shifter represents a feed-back signal derived from some form of temperature sensor, usually a thermistor or thermistor bridge, although more elaborate methods are possible.
The TXCO includes in the crystal resonator feed-back path carefully selected reactive components which are not voltage variable, but which have a temperature-characteristic response which exactly compensates for the temperature behavior of the crystal resonator resulting in a device exhibiting a minimal frequency-temperature dependence.
The third approach utilizes novel characteristics of crystal resonators to obtain temperature compensation without the use of an oven. U.S. Pat. No. 3,826,931 entitled "Dual Crystal Resonator Apparatus" filed in the name of Donald L. Hammond and issued on July 30, 1974, describes a resonator apparatus which utilizes either a single quartz crystal vibrating in two selected modes or two quartz crystals each vibrating in a single selected mode to form a resonator output frequency that is the sum or difference of the two crystal frequencies and is minimally temperature dependent.
All three approaches experience a significant drawback. The temperature compensation described is static compensation, that is, temperature compensation is achieved only under conditions where the ambient temperature is slowly changing. Rapidly changing temperatures sufficient to cause thermal gradients through the crystal resonator, cause instantaneous frequency shifts orders of magnitude greater than the static stability of the device. For example, the AT cut resonator in an oven can have short term stabilities which are several parts in 10.sup.10. However, a 1.degree. C. temperature gradient through the crystal resonator can cause a sudden frequency shift of 36 parts in 10.sup.6.
Dynamic compensation for thermal transients was recently discovered by Richard Holland. He predicted a doubly-rotated crystal resonator cut, the TS, that has an orientation of (yxwl) 22.8.degree./34.3.degree. (ANSI C83.3-1951 (R1972)) which exhibits inherently good frequency stability over a narrow temperature range suitable for obtaining good static compensation using either of the first two approaches discussed previously, and at the same time has inherent dynamic compensation for temperature transients. The TS orientation was introduced by Richard Holland in the following publications:
Richard Holland, "Nonuniformly Heated Anisotropic Plates: I. Mechanical Distortion and Relaxation", IEEE Transactions on Sonics and Ultrasonics, Vol. SU-21, July 1974, pp. 171-178, and Richard Holland, "Nonuniformly Heated Anisotropic Plates: II. Frequency Transients in AT and BT Quartz Plates," 1974 Ultrasonics Symposium Proceedings, IEEE Cat. #74CHO 896-15U, pp. 592-598.
At essentially the same time, another doubly-rotated crystal resonator cut, the SC, was predicted by Earl Eer Nisse to be (yxwl) 22.5.degree./34.3.degree., which is essentially the same as that predicted by Richard Holland. The SC orientation was introduced by Earl Eer Nisse in the following publication:
Earl E. Nisse, "Quartz Resonator Frequency Shifts Arising from Electrode Stress," Proceedings of the 29th Annual Symposium on Frequency Control 1975, U.S. Army Electronics Command, Fort Monmouth, N.J., May 28-30, 1975.
This cut exhibits the necessary frequency-temperature stability over narrow temperature ranges to obtain good static compensation with either the first or second approach. In addition, the SC is claimed to be frequency independent of internal stresses in the crystal resonator caused by deposited electrode patterns, crystal resonator mounts, and external applied stress in the plane of the crystal resonator surface. Both of these orientations offer thermal and mechanical stress sensitivity improvements over the AT and BT orientations but they still require operation in a controlled temperature environment over a narrow temperature range to achieve good frequency stability.